Hi Maureen
Just read this thread. I think Beannie very likely had the correct parents.
You may have done so in the intervening years, but if you find John McDOWALL's death registration, it should name his parents - assuming that the informant knew.
I see 2 possibilities on the Scotlandspeople index, one in Stranraer 1901, and one in Stoneykirk 1906.
I may be able to help you further, but will await your advice re how much more you have found since your last posting.
Bruce